Partition function P: Difference between revisions
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=={{header|Racket}}==
Backwards range was used to get responsive feedback for progress.
<lang racket>#lang racket
(require math/number-theory)
(define σ
(let ((memo (make-hash)))
(λ (z)
(hash-ref! memo z
(λ () (apply + (divisors z)))))))
(define p
(let ((memo (make-hash '((0 . 1)))))
(λ (n)
(hash-ref!
memo n
(λ ()
(let ((r (if (zero? n) 1
(/ (for/sum ((k (in-range (sub1 n) -1 -1)))
(* (σ (- n k))
(p k)))
n))))
(when (zero? (modulo n 1000)) (displayln (cons n r) (current-error-port)))
r))))))
(map p (range 1 30))
(p 666)
(p 1000)
(p 10000)</lang>
{{out}}
<pre>'(1 2 3 5 7 11 15 22 30 42 56 77 101 135 176 231 297 385 490 627 792 1002 1255 1575 1958 2436 3010 3718 4565)
11956824258286445517629485
(1000 . 24061467864032622473692149727991)
24061467864032622473692149727991
(2000 . 4720819175619413888601432406799959512200344166)
(3000 . 496025142797537184410324879054927095334462742231683423624)
(4000 . 1024150064776551375119256307915896842122498030313150910234889093895)
(5000 . 169820168825442121851975101689306431361757683049829233322203824652329144349)
(6000 . 4671727531970209092971024643973690643364629153270037033856605528925072405349246129)
(7000 . 32856930803440615786280925635924166861950151574532240659699032157432236394374450791229199)
(8000 . 78360264351568349490593145013364599719010769352985864331118600209417827764524450990388402844164)
(9000 . 77133638117808884907320791427403134961639798322072034262647713694605367979684296948790335590435626459)
(10000 . 36167251325636293988820471890953695495016030339315650422081868605887952568754066420592310556052906916435144)
36167251325636293988820471890953695495016030339315650422081868605887952568754066420592310556052906916435144</pre>
=={{header|Raku}}==
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